Monotone runs of uniformly distributed integer random variables: A probabilistic analysis

Programming Research Group A NOTE ON PROBABILISTIC INTEGER SORTING

We present a new probabilistic sequential algorithm for stable sorting n uniformly distributed keys in an arbitrary range. The algorithm runs in linear time with very-high probability 1 ? 2 ?(n) (the best previously known probability bound has been 1 ? 2 ?(n=(lg n lg lg n))). We also describe an EREW PRAM version of the algorithm that sorts in O((n=p + lg p) lg n= lg (n=p + lg n)) time using p ...

On a Probabilistic Property of the Fibonacci Sequence

Let 77l5..., 77w,... be a sequence of Independent integer-valued random variables. Let SnT]l + -~ + 7jn,Ari = ESn, B* = varS„,P„(m) = P(Sn = m), and f(t,rfj) denote the characteristic function of the random variable 77 •. The local limit theorem (LLT) is formulated as Pn(m) = (27rBy -exp{-(m^f /2B} + o(B~) when n-^00 uniformly for m. The first results on the normal approximation of binomial dis...

An improved reliability bound of a probabilistic parallel integer sorting algorithm

It is shown how one can improve the reliability bound of the parallel sorting algorithm of Rajasekaran and Sen [7] that sorts uniformly distributed integer keys on a CRCW Parallel Random Access Machine (PRAM). The probability of success improves to 1 − 2−Ω(n log logn/ logn) from the previous bound of 1 − 2−Ω(n/(logn log logn)) while retaining the Õ(log n) time bound for sorting n uniformly dist...

Ascending runs of sequences of geometrically distributed random variables: a probabilistic analysis

Network Location Problem with Stochastic and Uniformly Distributed Demands

This paper investigates the network location problem for single-server facilities that are subject to congestion. In each network edge, customers are uniformly distributed along the edge and their requests for service are assumed to be generated according to a Poisson process. A number of facilities are to be selected from a number of candidate sites and a single server is located at each facil...